day 1
day 2
4.3 investigating transformations
By the end of these lessons you will be able to:
- describe transformations of parabolas in vertex form
- write the equation of a parabola in vertex form
- identify the vertex, axis of symmetry, and the maximum or minimum point
Day 1 Video Tutorial: Investigating Transformations
Day 2 Video Tutorial: Describing transformations (part 1)
Day 2 video tutorial: Describing transformations (part 2)
Ontario Curriculum
Overall Expectations:
• determine the basic properties of quadratic relations;
• relate transformations of the graph of y = x2 to the algebraic representation y = a(x – h)2 + k;
• solve problems involving quadratic relations.
Specific Expectations:
- identify the key features of a graph of a parabola (i.e., the equation of the axis of symmetry, the coordinates of the vertex, the y-intercept, the zeros, and the maximum or minimum value)
- identify, through investigation using technology, the effect on the graph of y = x2 of transformations (i.e., translations, reflections in the x-axis, vertical stretches or compressions) by considering separately each parameter a, h, and k
- explain the roles of a, h, and k in y = a(x – h )2 + k, using the appropriate terminology to describe the transformations, and identify the vertex and the equation of the axis of symmetry;
- sketch, by hand, the graph of y = a(x – h )2 + k by applying Transformations to the graph of y = x2